5 Colo. Code Regs. § 1002-31-A
The biologically-based flow calculation method is an iterative convergence procedure consisting of five parts. In Part I, Z (the allowed number of excursions) is calculated. In Part II, the set of X-day running averages is calculated from the daily flows for the period of record being considered. Because the ambient (instream) concentration of a pollutant can be considered to be inversely proportional to stream flow, the appropriate "running averages" of stream flow are actually "running harmonic means." (The harmonic mean of a set of numbers is the reciprocal of the arithmetic mean of the reciprocals of the numbers.) Thus, "X-day running averages" should be calculated as , not as , where F is the flow for an individual day. Throughout this Appendix A, the term "running average" will mean "running harmonic mean."
Part III describes the calculation of N (the total number of excursions of a specified flow for the period of record being considered). The calculations described in Part III will be performed for a number of different flows that are specified in Parts IV and V. In Part IV, initial lower and upper limits on the flow are calculated, the number of excursions at each limit are calculated using Part III, and an initial trial flow is calculated by interpolation between the lower and upper limits. In Part V, successive iterations are performed to calculate the flow as the highest flow that results in no more than the number of allowed excursions calculated in Part I.
Part I. Calculation of allowed number of excursions.
I-1. Calculate Z = D/[(Y)(365.25 days/year])
where D = the number of days in the flow record;
Y = the average number of years specified in the frequency; and
Z = the allowed number of excursions based on a 1-in-3-year recurrence interval.
Part II. Calculation of X-day running averages, i.e., X-day running harmonic means.
II-1. Where X = the specified duration (in days) of the averaging period, calculate the set of X-day running averages for the entire period of record being considered, i.e., calculate an X-day average starting with day 1, day 2, day 3, etc. Each average will have X-1 days in common with the next average, and the number of X-day averages calculated from the period of record being considered will be (D+1-X).
Part III. Determination of the number of excursions of a specified flow in a set of running averages, i.e., running harmonic means.
III-1. Select a specified trial low flow by method outlined in Part IV or an equivalent method.
III-2. In the set of X-day running averages for the period of record being considered, record the date for which the first average is below the specified trial low flow and record the number of consecutive days that are part of at least one or more of the X-day averages that are below the specified flow. (Note that whether a day is counted as an excursion day does not depend exclusively on whether the X-day average for that day is below the specified trial low flow. Instead, it depends entirely on whether that day is part of any X-day average that is below the specified trial low flow. Table A-1 provides examples of the counting of excursion days. For ease in discussion, it is based on a 4-day flow period, rather than a 30-day flow period. When calculating a low flow pursuant to Section 31.9 , a 30-day period should be used.)
Thus the starting date and the duration (in days) of the first excursion period will be recorded. By definition, the minimum duration is X days.
III-3. Determine the starting dates of, and number of days in, each succeeding excursion period in the period of record being considered.
III-4. Identify all of the excursion periods that begin within 120 days after the beginning of the first excursion period. (Although the first excursion period is often the only one in the 120-day period, two or three sometimes occur within the 120 days. Rarely do any excursion periods occur during days 121 to 240.) All of these excursion periods are considered to be in the first low flow period. Add up the total number of excursion days in the first low flow period and divide the sum by X to obtain the number of excursions in the first low flow period. If the number of excursions is calculated to be greater than 5.0, set it equal to 5.0.
III-5. Identify the first excursion period that begins after the end of the first low flow period, and start the beginning of the second 120-day low flow period on the first day of this excursion period. Determine the number of excursion days and excursions in the second low flow period.
III-6. Determine the starting dates of, and the number of excursions in, each succeeding 120-day low flow period.
III-7. Sum the number of excursions in all the low-flow periods to determine S = the total number of excursions of the specified trial low flow.
Part IV. Calculation of initial limits of the low flow and initial trial flow.
IV-1. Use L = 0 as the initial lower limit.
IV-2. Use U = the XQY low flow as the initial upper limit.
IV-3. Use N L = 0 as the number of excursions (see Part III) of the initial lower limit.
IV-4. Calculate N U = the number of excursions (see Part III) of the initial upper limit.
IV-6. Calculation of initial limits of the low flow and initial trial flow may be accomplished using equivalent methods.
Part V. Iterative convergence to the low flow.
V-1. Calculate N T = the number of excursions for the trial low flow.
If -0.005 < (NT - Z) /Z)< +.005
If NT >Z, set U = Tand NU=NT.
V-2 if NT <Z set L = T and NL= NT. , use T as the low flow and stop.
V-3. If ((U-L)/U) < 0.005, use L as the low flow and stop.
APPENDIX A TABLE A-1 - COUNTING EXCURSION DAYS FOR A SPECIFIED FLOW OF 100 FT3/SEC USING 4-DAY AVERAGES.
TABLE A-1. COUNTING EXCURSION DAYS FOR A SPECIFIED FLOW OF 100 FT3/SEC USING 4-DAY AVERAGES. | |||||||||
Date | Daily flow | 4-day avg. flow | Is the 4-day average below 100? | Is this date part of any 4-day average that is below 100? | Date of start of excursion period | Number of days in excursion period | Date of start of low flow period | Number of excursion days in low flow period | Number or excursions in low flow period |
1 | 130 | 112.5 | No | No | |||||
2 | 120 | 102.5 | No | No | |||||
3 | 110 | 97.5 | Yes | Yes | 3 | 4 | 3 | 12 | 3 |
4 | 90 | 102.5 | No | Yes | |||||
5 | 90 | 117.5 | No | Yes | |||||
6 | 100 | 112.5 | No | Yes | |||||
7 | 130 | 102.5 | No | No | |||||
8 | 150 | 102.5 | No | No | |||||
9 | 70 | 87.5 | Yes | Yes | 9 | 8 | |||
10 | 60 | 90.0 | Yes | Yes | |||||
11 | 130 | 102.5 | No | Yes | |||||
12 | 90 | 95.0 | Yes | Yes | |||||
13 | 80 | 97.5 | Yes | Yes | |||||
14 | 110 | 127.5 | No | Yes | |||||
15 | 100 | 225.0 | No | Yes | |||||
16 | 100 | >100 | No | Yes | |||||
17 | 200 | >100 | No | No | |||||
18 | 500 | >100 | No | No | |||||
The daily flows and four-day average flows for days 19 to 200 are all above 100 ft3/sec. | |||||||||
5 CCR 1002-31-A